The temperature of sun is 5500 K and it emits maximum intensity radiation in the yellow region`(5.5 xx10^(-7)m)`. The maximum radiation from a furnace occurs at wavelength `11 xx 10^(-7)m` The temperature of furnace is

Options

A. 500 K
B. 1750 K
C. 3750 K
D. 2750 K

Answer

To solve the problem, we will use Wien's Displacement Law, which states that the product of the wavelength at which the emission of radiation is maximum (λ_max) and the absolute temperature (T) of the black body is a constant. This can be expressed mathematically as:

\[ \lambda_{M1} \cdot T1 = \lambda_{M2} \cdot T2 \]

Where:
- \( \lambda_{M1} \) is the maximum wavelength of the sun's radiation,
- \( T1 \) is the temperature of the sun,
- \( \lambda_{M2} \) is the maximum wavelength of the furnace's radiation,
- \( T2 \) is the temperature of the furnace.

### Step 1: Identify the known values
From the problem statement, we have:
- \( \lambda_{M1} = 5.5 \times 10^{-7} \, m \) (wavelength of the sun)
- \( T1 = 5500 \, K \) (temperature of the sun)
- \( \lambda_{M2} = 11 \times 10^{-7} \, m \) (wavelength of the furnace)

### Step 2: Substitute the known values into the equation
Using the equation from Wien's Displacement Law:

\[ (5.5 \times 10^{-7} \, m) \cdot (5500 \, K) = (11 \times 10^{-7} \, m) \cdot T2 \]

### Step 3: Simplify the equation
We can cancel \( 10^{-7} \) from both sides:

\[ 5.5 \cdot 5500 = 11 \cdot T2 \]

### Step 4: Calculate the left side
Calculating \( 5.5 \cdot 5500 \):

\[ 5.5 \cdot 5500 = 30250 \]

### Step 5: Solve for \( T2 \)
Now we can solve for \( T2 \):

\[ 30250 = 11 \cdot T2 \]

Dividing both sides by 11:

\[ T2 = \frac{30250}{11} \]

Calculating \( T2 \):

\[ T2 = 2750 \, K \]

### Final Answer
The temperature of the furnace is \( 2750 \, K \).

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